## Admissible Graph Rewriting and Narrowing (1998)

Venue: | IN PROCEEDINGS OF THE JOINT INTERNATIONAL CONFERENCE AND SYMPOSIUM ON LOGIC PROGRAMMING |

Citations: | 29 - 6 self |

### BibTeX

@INPROCEEDINGS{Echahed98admissiblegraph,

author = {Rachid Echahed and Jean-christophe Janodet},

title = {Admissible Graph Rewriting and Narrowing},

booktitle = {IN PROCEEDINGS OF THE JOINT INTERNATIONAL CONFERENCE AND SYMPOSIUM ON LOGIC PROGRAMMING},

year = {1998},

pages = {325--340},

publisher = {MIT Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

We address the problem of graph rewriting and narrowing as the underlying operational semantics of rule-based programming languages. We propose new optimal graph rewriting and narrowing strategies in the setting of orthogonal constructor-based graph rewriting systems. For this purpose, we first characterize a subset of graphs, called admissible graphs. A graph is admissible if none of its defined operations belongs to a cycle. We then prove the confluence, as well as the confluence modulo bisimilarity (unraveling), of the admissible graph rewriting relation. Afterwards, we define a sequential graph rewriting strategy by using Antoy’s definitional trees. We show that the resulting strategy computes only needed redexes and develops optimal derivations w.r.t. the number of steps. Finally, we tackle the graph narrowing relation over admissible graphs and propose a sequential narrowing strategy which computes independent solutions and develops shorter derivations than most general graph narrowing.

### Citations

334 | Functional logic programming: From theory to Curry
- Hanus
- 2013
(Show Context)
Citation Context ...ops shorter derivations than most general graph narrowing. 1 Introduction Many efforts have been dedicated to investigate the integration of functional and logic languages during the last decade, see =-=[11]-=- for a survey and [18, 12] for recent language propositions. The underlying operational semantics of such languages is often based on first-order term rewriting and narrowing. In practice, data struct... |

291 | A needed narrowing strategy
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(Show Context)
Citation Context ...of admissible graphs and develops shortest derivations. Narrowing [14] has been intensively investigated during the last decade in the framework of TRSs. An optimal narrowing strategy is presented in =-=[2]-=-. However, to our knowledge, only few studies considered the extension of narrowing to graphs [9, 21, 10]. In these papers the considered graphs are acyclic and the best known strategy is basic narrow... |

166 |
Canonical forms and unification
- Hullot
- 1980
(Show Context)
Citation Context ...uctor-based GRSs with the same nice properties. We particularly prove that the resulting strategy is c-hyper-normalizing on the class of admissible graphs and develops shortest derivations. Narrowing =-=[14]-=- has been intensively investigated during the last decade in the framework of TRSs. An optimal narrowing strategy is presented in [2]. However, to our knowledge, only few studies considered the extens... |

152 | Definitional trees
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- 1992
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Citation Context ...ressions in a deterministic and efficient way by using rewriting strategies. Such strategies have been well investigated in the setting of finite and infinite orthogonal TRSs (e.g., [19, 13, 16]). In =-=[1]-=-, a strategy that computes outermost needed redexes based on definitional trees has been designed in the framework of orthogonal constructor-based TRSs. In this article, we show that Antoy’s strategy ... |

129 |
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- 1993
(Show Context)
Citation Context ... implementation by pattern-matching. In [17], a lazy graph rewriting strategy close to ours is described, namely the annotated functional strategy, which combines the discriminating position strategy =-=[20]-=- and rewriting with priority [4]. To our knowledge, no formal result has been proved regarding this strategy. In addition, we considered the extension of narrowing to admissible graphs and established... |

106 |
graph rewriting
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Citation Context ...erature to investigate graph rewriting [8, 22]. The aim of this section is to recall briefly some key definitions in order to make easier the understanding of the paper. We are mostly consistent with =-=[5]-=-. A many-sorted signature Σ = 〈S, Ω〉 consists of a set S of sorts and an S-indexed family of sets of operation symbols Ω = ⊎s∈SΩs with Ωs = ⊎ (w,s)∈S ∗ ×SΩw,s. We shall write f : s1 . . .sn → s whenev... |

86 |
Computing in Systems Described by Equations
- O’DONNELL
- 1977
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Citation Context ...ws to evaluate expressions in a deterministic and efficient way by using rewriting strategies. Such strategies have been well investigated in the setting of finite and infinite orthogonal TRSs (e.g., =-=[19, 13, 16]-=-). In [1], a strategy that computes outermost needed redexes based on definitional trees has been designed in the framework of orthogonal constructor-based TRSs. In this article, we show that Antoy’s ... |

70 | Klop: Equational Term Graph Rewriting
- Ariola, W
- 1996
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Citation Context .... A term graph is a (possibly cyclic) graph with one root denoted Rootg. Two term graphs g1 and g2 are bisimilar, denoted g1 . = g2, iff they represent the same (infinite) tree when one unravels them =-=[3]-=-. We write g1 ∼ g2 whenever the term graphs g1 and g2 are equal up to renaming of nodes. As the formal definition of graphs is not useful to give examples, we introduce a linear notation [5]. In the f... |

64 |
Computations in orthogonal term rewriting systems
- Huet, Lévy
- 1991
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Citation Context ...ws to evaluate expressions in a deterministic and efficient way by using rewriting strategies. Such strategies have been well investigated in the setting of finite and infinite orthogonal TRSs (e.g., =-=[19, 13, 16]-=-). In [1], a strategy that computes outermost needed redexes based on definitional trees has been designed in the framework of orthogonal constructor-based TRSs. In this article, we show that Antoy’s ... |

52 |
de Vries. Transfinite reductions in orthogonal term rewriting
- Kennaway, Klop, et al.
- 1995
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Citation Context ...ws to evaluate expressions in a deterministic and efficient way by using rewriting strategies. Such strategies have been well investigated in the setting of finite and infinite orthogonal TRSs (e.g., =-=[19, 13, 16]-=-). In [1], a strategy that computes outermost needed redexes based on definitional trees has been designed in the framework of orthogonal constructor-based TRSs. In this article, we show that Antoy’s ... |

21 |
De Vries. On the adequacy of graph rewriting for simulating term rewriting
- Kennaway, Klop, et al.
- 1994
(Show Context)
Citation Context ...is a variable. This rule, which constitutes an orthogonal TRS, generates a confluent rewrite relation over (finite or infinite) terms whereas it generates a non confluent rewrite relationsover graphs =-=[15]-=-. It is well-known that this source of nonconfluency of GRSs comes from the so-called “collapsing rules” in orthogonal GRSs. A rewrite rule is collapsing if its right-hand side is a variable. However,... |

16 | On constructor-based graph rewriting systems
- Echahed, Janodet
- 1997
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Citation Context ...a sequential narrowing strategy and list its properties. Due to lack of space, some detailed definitions and all the proofs are omitted from this paper. Precise definitions and proofs can be found in =-=[7, 6]-=-. 2 Preliminaries Many different notations are used in the literature to investigate graph rewriting [8, 22]. The aim of this section is to recall briefly some key definitions in order to make easier ... |

13 | Computing by graph transformation : A survey and annotated bibliography
- Ehrig, Taentzer
- 1996
(Show Context)
Citation Context ...d all the proofs are omitted from this paper. Precise definitions and proofs can be found in [7, 6]. 2 Preliminaries Many different notations are used in the literature to investigate graph rewriting =-=[8, 22]-=-. The aim of this section is to recall briefly some key definitions in order to make easier the understanding of the paper. We are mostly consistent with [5]. A many-sorted signature Σ = 〈S, Ω〉 consis... |

13 |
An Integrated Functional Logic Language. Available at: http://www.informatik.uni-kiel.de/~curry
- Curry
- 2000
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Citation Context ...s than most general graph narrowing. 1 Introduction Many efforts have been dedicated to investigate the integration of functional and logic languages during the last decade, see [11] for a survey and =-=[18, 12]-=- for recent language propositions. The underlying operational semantics of such languages is often based on first-order term rewriting and narrowing. In practice, data structures are represented as (c... |

12 | Term Graph Narrowing
- Habel, Plump
- 1996
(Show Context)
Citation Context ...tigated during the last decade in the framework of TRSs. An optimal narrowing strategy is presented in [2]. However, to our knowledge, only few studies considered the extension of narrowing to graphs =-=[9, 21, 10]-=-. In these papers the considered graphs are acyclic and the best known strategy is basic narrowing. In the present paper, we investigate most general narrowing on admissible (cyclic) graphs and establ... |

9 |
Term rewriting systems with priorities
- Baeten, Bergstra, et al.
- 1987
(Show Context)
Citation Context ...ng. In [17], a lazy graph rewriting strategy close to ours is described, namely the annotated functional strategy, which combines the discriminating position strategy [20] and rewriting with priority =-=[4]-=-. To our knowledge, no formal result has been proved regarding this strategy. In addition, we considered the extension of narrowing to admissible graphs and established the completeness and the soundn... |

7 |
Graph rewriting using the annotated functional strategy
- Koopman, Smetsers, et al.
- 1993
(Show Context)
Citation Context ...ch is c-normalizing and optimal for the class of admissible graphs. The use of definitional trees allows to combine the elegance of neededness with an efficient implementation by pattern-matching. In =-=[17]-=-, a lazy graph rewriting strategy close to ours is described, namely the annotated functional strategy, which combines the discriminating position strategy [20] and rewriting with priority [4]. To our... |

4 |
Completeness results for basic narrowing in non-copying implementations
- Rao
- 1996
(Show Context)
Citation Context ...tigated during the last decade in the framework of TRSs. An optimal narrowing strategy is presented in [2]. However, to our knowledge, only few studies considered the extension of narrowing to graphs =-=[9, 21, 10]-=-. In these papers the considered graphs are acyclic and the best known strategy is basic narrowing. In the present paper, we investigate most general narrowing on admissible (cyclic) graphs and establ... |

2 |
Introducing graphs in functional logic programming languages
- Echahed, Janodet
- 1997
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Citation Context ...a sequential narrowing strategy and list its properties. Due to lack of space, some detailed definitions and all the proofs are omitted from this paper. Precise definitions and proofs can be found in =-=[7, 6]-=-. 2 Preliminaries Many different notations are used in the literature to investigate graph rewriting [8, 22]. The aim of this section is to recall briefly some key definitions in order to make easier ... |

2 |
Completeness of narrowing in non-copying implementations
- Habel, Plump
- 1997
(Show Context)
Citation Context ...tigated during the last decade in the framework of TRSs. An optimal narrowing strategy is presented in [2]. However, to our knowledge, only few studies considered the extension of narrowing to graphs =-=[9, 21, 10]-=-. In these papers the considered graphs are acyclic and the best known strategy is basic narrowing. In the present paper, we investigate most general narrowing on admissible (cyclic) graphs and establ... |

2 |
Combining functional and logic languages
- Lloyd
- 1994
(Show Context)
Citation Context ...s than most general graph narrowing. 1 Introduction Many efforts have been dedicated to investigate the integration of functional and logic languages during the last decade, see [11] for a survey and =-=[18, 12]-=- for recent language propositions. The underlying operational semantics of such languages is often based on first-order term rewriting and narrowing. In practice, data structures are represented as (c... |